Types of Piecewise functions Step Functions functions made

Types of Piecewise functions • Step Functions: • functions made up of Horizontal line segments with a closed circle on one end an open circle on the other. • The graph looks like a set of steps Absolute Value Functions: V-shaped grapg

Absolute Value Function- V- Shaped graph.

The graph of this piecewise function consists of 2 rays, is V-shaped and opens up. To the left of x=0 the line is y = -x To the right of x = 0 the line is y=x

Write absolute value function as a piecewise function • •

Graphing Absolute Value functions f(x) = a |x - h| + k • Vertex is (h, k) • AOS: x=h • If a< 0 the graph opens down (a is negative) • If a>0 the graph opens up (a is positive) • The graph is wider if |a| < 1 (fraction < 1) • The graph is narrower if |a| > 1 • a is the slope to the right of the vertex (…-a is the slope to the left of the vertex)

Graph y = -|x + 2| + 3 1. V = (-2, 3) 2. Apply the slope a=-1 to that point 3. Use the line of symmetry x=-2 to plot the 3 rd point. 4. Complete the graph

Graph y = -|x - 1| + 1

Write the equation for:

• The vertex is @ (0, -3) • It has the form: • y = a |x - 0| - 3 So the equation is: y = 2|x| -3 • To find a: substitute the coordinate of a point (2, 1) in and solve • (or count the slope from the vertex to another point to the right) • Remember: a is positive if the graph goes up • a is negative if the graph goes down